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Indestructible guessing models and the continuum

Volume 239 / 2017

Sean Cox, John Krueger Fundamenta Mathematicae 239 (2017), 221-258 MSC: 03E05, 03E35, 03E40, 03E65. DOI: 10.4064/fm340-1-2017 Published online: 26 May 2017


We introduce a stronger version of an $\omega _1$-guessing model, which we call an indestructibly $\omega _1$-guessing model. The principle $\mathsf {IGMP}$ states that there are stationarily many indestructibly $\omega _1$-guessing models. This principle, which follows from $\mathsf {PFA}$, captures many of the consequences of $\mathsf {PFA}$, including the Suslin hypothesis and the singular cardinal hypothesis. We prove that $\mathsf {IGMP}$ is consistent with the continuum being arbitrarily large.


  • Sean CoxDepartment of Mathematics and Applied Mathematics
    Virginia Commonwealth University
    1015 Floyd Avenue
    P.O. Box 842014
    Richmond, VA 23284, U.S.A.
  • John KruegerDepartment of Mathematics
    University of North Texas
    1155 Union Circle #311430
    Denton, TX 76203, U.S.A.

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